In a context-free grammar G, if there is a production in the form X в†’ Xa where X is a non-terminal and вЂaвЂ™ is a string of terminals, it is called a left recursive production. The stepwise derivation of the above string is shown as below в€’ Left and Right Recursive Grammars The rightmost derivation for the above string 'a+a*a' may be в€’ The stepwise derivation of the above string is shown as below в€’ The leftmost derivation for the string 'a+a*a' may be в€’ Let any set of production rules in a CFG be Rightmost derivation в€’ A rightmost derivation is obtained by applying production to the rightmost variable in each step. Leftmost derivation в€’ A leftmost derivation is obtained by applying production to the leftmost variable in each step. Leftmost and Rightmost Derivation of a String The above sub-tree is also in sentential form. If a partial derivation tree contains the root S, it is called a sentential form. The partial derivation tree can be the following в€’ S в†’ SS в†’ aSbS в†’ abS в†’ abaSb в†’ abaaSbb в†’ abaabb Sentential Form and Partial Derivation TreeДЄ partial derivation tree is a sub-tree of a derivation tree/parse tree such that either all of its children are in the sub-tree or none of them are in the sub-tree. One derivation from the above CFG is вЂњabaabbвЂќ The grammar (, Starting symbol = S, P = S в†’ SS | aSb | Оµ.

P is a set of rules, P: N в†’ (N в€Є T)*, i.e., the left-hand side of the production rule P does have any right context or left context. T is a set of terminals where N в€© T = NULL.

Definition в€’ A context-free grammar (CFG) consisting of a finite set of grammar rules is a quadruple (N, T, P, S) where

Context-free grammar checker